Probably this example about One-degree-of-freedom direct-solution and subspace-based steady-state dynamic analysis with hysteretic damping will help you:

https://classes.engineering.wustl.edu/2009/spring/mase5513/abaqus/docs/v6.6/books/eif/vibration_1dof_ssdyn_hyster.inp

Hello Amir

Hysteristic or internal damping is very much different from structural damping. Hysteristic damping is due to energy dissipation due to friction between parts of a structure as a structure vibrates.

Structural damping is damping that arises from a combination of the mass and stiffness of a structure.

More info follows.

Amaechi J. Anyaegbunam Thanks for your reply.

So how can I use hysteretic damping in Abaqus?

Dear Amir,

I think you can find answer to your question in my paper below

Article Seismic Design of Subsea Jumper per ISO: Part I-Preliminaries

Please also have a look at the reminder of the above paper

Article Seismic Design of Subsea Spools per ISO: Part II-Seismic Requirements

Article Seismic Design of Subsea Spool per ISO: Part III-Analysis & Design

Please write back if the answer that you are seeking is not there.

Best regards

Sirous

Dear Amir,

I think you have at least three possibilities:

(i) viscoelastic model; (ii) elastic-plastic model and (iii) hyperelastic Arruda - Boyce model especially designed for modelling hysteretic behavior;

while these models are referred to different phenomena (the first associates with viscous friction, second refers to dry friction, and third associates with polymers) all of them can be used for modelling hysteretic behavior.

All these models are available in Abaqus.

See some examples for case (ii),

Code 3d-cube-static-kinematic

Code 3d cube made of the Modified Cam-Clay (MCC) model at kinemat...

Hi

It should be possible to use this damping model in Abaqus

https://abaqus-docs.mit.edu/2017/English/SIMACAEMATRefMap/simamat-c-dampingopt.htm#simamat-c-dampingopt-structural

However, be advised that you may ruin causality when using structural damping in the time domain.

/Claes

Hi Amir

Was my answer relevant to your question?

Dear Professor Sirous Yasseri

Thanks for your response and useful information.

Unfortunately, I could not apply the material hysteretic damping ratio to Abaqus and still confused about that.

Hi Amir,

Are you trying to apply various material properties to various soil layers?

Yes Professor Sirous Yasseri

Applying various material properties to various soil layers and tunnel.